Kepler by Walter W Bryant

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Title: Kepler

Author: Walter W. Bryant

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Language: English

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Kepler

PIONEERS OF PROGRESS

MEN OF SCIENCE

EDITED BY S. CHAPMAN, M.A., D.SC., F.R.S.

KEPLER

BY

WALTER W. BRYANT

OF THE ROYAL OBSERVATORY, GREENWICH

1920

CONTENTS.

I. ASTRONOMY BEFORE KEPLER
II. EARLY LIFE OF KEPLER
III. TYCHO BRAHE
IV. KEPLER JOINS TYCHO
V. KEPLER’S LAWS
VI. CLOSING YEARS
APPENDIX I.—LIST OF DATES
APPENDIX II.—BIBLIOGRAPHY
GLOSSARY

CHAPTER I.

ASTRONOMY BEFORE KEPLER.

In order to emphasise the importance of the reforms introduced into astronomy by Kepler, it will be well to sketch briefly the history of the

theories which he had to overthrow. In very early times it must have been realised that the sun and moon were continually changing their places
among the stars. The day, the month, and the year were obvious divisions of time, and longer periods were suggested by the tabulation of eclipses.
We can imagine the respect accorded to the Chaldaean sages who first discovered that eclipses could be predicted, and how the philosophers of
Mesopotamia must have sought eagerly for evidence of fresh periodic laws. Certain of the stars, which appeared to wander, and were hence
called planets, provided an extended field for these speculations. Among the Chaldaeans and Babylonians the knowledge gradually acquired was
probably confined to the priests and utilised mainly for astrological prediction or the fixing of religious observances. Such speculations as were
current among them, and also among the Egyptians and others who came to share their knowledge, were almost entirely devoted to mythology,
assigning fanciful terrestrial origins to constellations, with occasional controversies as to how the earth is supported in space. The Greeks, too, had
an elaborate mythology largely adapted from their neighbours, but they were not satisfied with this, and made persistent attempts to reduce the
apparent motions of celestial objects to geometrical laws. Some of the Pythagoreans, if not Pythagoras himself, held that the earth is a sphere, and
that the apparent daily revolution of the sun and stars is really due to a motion of the earth, though at first this motion of the earth was not supposed
to be one of rotation about an axis. These notions, and also that the planets on the whole move round from west to east with reference to the stars,
were made known to a larger circle through the writings of Plato. To Plato moreover is attributed the challenge to astronomers to represent all the
motions of the heavenly bodies by uniformly described circles, a challenge generally held responsible for a vast amount of wasted effort, and the
postponement, for many centuries, of real progress. Eudoxus of Cnidus, endeavouring to account for the fact that the planets, during every

apparent revolution round the earth, come to rest twice, and in the shorter interval between these “stationary points,” move in the opposite
direction, found that he could represent the phenomena fairly well by a system of concentric spheres, each rotating with its own velocity, and
carrying its own particular planet round its own equator, the outermost sphere carrying the fixed stars. It was necessary to assume that the axes
about which the various spheres revolved should have circular motions also, and gradually an increased number of spheres was evolved, the total
number required by Aristotle reaching fifty-five. It may be regarded as counting in Aristotle’s favour that he did consider the earth to be a sphere
and not a flat disc, but he seems to have thought that the mathematical spheres of Eudoxus had a real solid existence, and that not only meteors,
shooting stars and aurora, but also comets and the milky way belong to the atmosphere. His really great service to science in collating and
criticising all that was known of natural science would have been greater if so much of the discussion had not been on the exact meaning of words
used to describe phenomena, instead of on the facts and causes of the phenomena themselves.

Aristarchus of Samos seems to have been the first to suggest that the planets revolved not about the earth but about the sun, but the idea

seemed so improbable that it was hardly noticed, especially as Aristarchus himself did not expand it into a treatise.

About this time the necessity for more accurate places of the sun and moon, and the liberality of the Ptolemys who ruled Egypt, combined to

provide regular observations at Alexandria, so that, when Hipparchus came upon the scene, there was a considerable amount of material for him to
use. His discoveries marked a great advance in the science of astronomy. He noted the irregular motion of the sun, and, to explain it, assumed that
it revolved uniformly not exactly about the earth but about a point some distance away, called the “excentric”. [1] The line joining the centre of the
earth to the excentric passes through the apses of the sun’s orbit, where its distance from the earth is greatest and least. The same result he could
obtain by assuming that the sun moved round a small circle, whose centre described a larger circle about the earth; this larger circle carrying the
other was called the “deferent”: so that the actual motion of the sun was in an epicycle. Of the two methods of expression Hipparchus ultimately
preferred the second. He applied the same process to the moon but found that he could depend upon its being right only at new and full moon. The
irregularity at first and third quarters he left to be investigated by his successors. He also considered the planetary observations at his disposal
insufficient and so gave up the attempt at a complete planetary theory. He made improved determinations of some of the elements of the motions of
the sun and moon, and discovered the Precession of the Equinoxes, from the Alexandrian observations which showed that each year as the sun
came to cross the equator at the vernal equinox it did so at a point about fifty seconds of arc earlier on the ecliptic, thus producing in 150 years an
unmistakable change of a couple of degrees, or four times the sun’s diameter. He also invented trigonometry. His star catalogue was due to the
appearance of a new star which caused him to search for possible previous similar phenomena, and also to prepare for checking future ones. No
advance was made in theoretical astronomy for 260 years, the interval between Hipparchus and Ptolemy of Alexandria. Ptolemy accepted the
spherical form of the earth but denied its rotation or any other movement. He made no advance on Hipparchus in regard to the sun, though the
lapse of time had largely increased the errors of the elements adopted by the latter. In the case of the moon, however, Ptolemy traced the variable
inequality noticed sometimes by Hipparchus at first and last quarter, which vanished when the moon was in apogee or perigee. This he called the
evection, and introduced another epicycle to represent it. In his planetary theory he found that the places given by his adopted excentric did not fit,
being one way at apogee and the other at perigee; so that the centre of distance must be nearer the earth. He found it best to assume the centre of
distance half-way between the centre of the earth and the excentric, thus “bisecting the excentricity”. Even this did not fit in the case of Mercury,
and in general the agreement between theory and observation was spoilt by the necessity of making all the orbital planes pass through the centre of
the earth, instead of the sun, thus making a good accordance practically impossible.

Footnote 1: See Glossary for this and other technical terms.

After Ptolemy’s time very little was heard for many centuries of any fresh planetary theory, though advances in some points of detail were

made, notably by some of the Arab philosophers, who obtained improved values for some of the elements by using better instruments. From time
to time various modifications of Ptolemy’s theory were suggested, but none of any real value. The Moors in Spain did their share of the work
carried on by their Eastern co-religionists, and the first independent star catalogue since the time of Hipparchus was made by another Oriental,
Tamerlane’s grandson, Ulugh Begh, who built a fine observatory at Samarcand in the fifteenth century. In Spain the work was not monopolised by
the Moors, for in the thirteenth century Alphonso of Castile, with the assistance of Jewish and Christian computers, compiled the Alphonsine
tables, completed in 1252, in which year he ascended the throne as Alphonso X. They were long circulated in MS. and were first printed in 1483,
not long before the end of the period of stagnation.

Copernicus was born in 1473 at Thorn in Polish Prussia. In the course of his studies at Cracow and at several Italian universities, he learnt all

that was known of the Ptolemaic astronomy and determined to reform it. His maternal uncle, the Bishop of Ermland, having provided him with a
lay canonry in the Cathedral of Frauenburg, he had leisure to devote himself to Science. Reviewing the suggestions of the ancient Greeks, he was
struck by the simplification that would be introduced by reviving the idea that the annual motion should be attributed to the earth itself instead of
having a separate annual epicycle for each planet and for the sun. Of the seventy odd circles or epicycles required by the latest form of the
Ptolemaic system, Copernicus succeeded in dispensing with rather more than half, but he still required thirty-four, which was the exact number
assumed before the time of Aristotle. His considerations were almost entirely mathematical, his only invasion into physics being in defence of the
“moving earth” against the stock objection that if the earth moved, loose objects would fly off, and towers fall. He did not break sufficiently away
from the old tradition of uniform circular motion. Ptolemy’s efforts at exactness were baulked, as we have seen, by the supposed necessity of all
the orbit planes passing through the earth, and if Copernicus had simply transferred this responsibility to the sun he would have done better. But he
would not sacrifice the old fetish, and so, the orbit of the earth being clearly not circular with respect to the sun, he made all his planetary planes
pass through the centre of the earth’s orbit, instead of through the sun, thus handicapping himself in the same way though not in the same degree as
Ptolemy. His thirty-four circles or epicycles comprised four for the earth, three for the moon, seven for Mercury (on account of his highly eccentric
orbit) and five each for the other planets.

It is rather an exaggeration to call the present accepted system the Copernican system, as it is really due to Kepler, half a century after the

death of Copernicus, but much credit is due to the latter for his successful attempt to provide a real alternative for the Ptolemaic system, instead of
tinkering with it. The old geocentric system once shaken, the way was gradually smoothed for the heliocentric system, which Copernicus, still
hampered by tradition, did not quite reach. He was hardly a practical astronomer in the observational sense. His first recorded observation, of an
occultation of Aldebaran, was made in 1497, and he is not known to have made as many as fifty astronomical observations, while, of the few he
did make and use, at least one was more than half a degree in error, which would have been intolerable to such an observer as Hipparchus.

Copernicus in fact seems to have considered accurate observations unattainable with the instruments at hand. He refused to give any opinion on the
projected reform of the calendar, on the ground that the motions of the sun and moon were not known with sufficient accuracy. It is possible that
with better data he might have made much more progress. He was in no hurry to publish anything, perhaps on account of possible opposition.
Certainly Luther, with his obstinate conviction of the verbal accuracy of the Scriptures, rejected as mere folly the idea of a moving earth, and
Melanchthon thought such opinions should be prohibited, but Rheticus, a professor at the Protestant University of Wittenberg and an enthusiastic
pupil of Copernicus, urged publication, and undertook to see the work through the press. This, however, he was unable to complete and another
Lutheran, Osiander, to whom he entrusted it, wrote a preface, with the apparent intention of disarming opposition, in which he stated that the
principles laid down were only abstract hypotheses convenient for purposes of calculation. This unauthorised interpolation may have had its share
in postponing the prohibition of the book by the Church of Rome.

According to Copernicus the earth is only a planet like the others, and not even the biggest one, while the sun is the most important body in

the system, and the stars probably too far away for any motion of the earth to affect their apparent places. The earth in fact is very small in
comparison with the distance of the stars, as evidenced by the fact that an observer anywhere on the earth appears to be in the middle of the
universe. He shows that the revolution of the earth will account for the seasons, and for the stationary points and retrograde motions of the planets.
He corrects definitely the order of the planets outwards from the sun, a matter which had been in dispute. A notable defect is due to the idea that a
body can only revolve about another body or a point, as if rigidly connected with it, so that, in order to keep the earth’s axis in a constant direction
in space, he has to invent a third motion. His discussion of precession, which he rightly attributes to a slow motion of the earth’s axis, is marred by
the idea that the precession is variable. With all its defects, partly due to reliance on bad observations, the work showed a great advance in the
interpretation of the motions of the planets; and his determinations of the periods both in relation to the earth and to the stars were adopted by
Reinhold, Professor of Astronomy at Wittenberg, for the new Prutenic or Prussian Tables, which were to supersede the obsolete Alphonsine
Tables of the thirteenth century.

In comparison with the question of the motion of the earth, no other astronomical detail of the time seems to be of much consequence.

Comets, such as from time to time appeared, bright enough for naked eye observation, were still regarded as atmospheric phenomena, and their
principal interest, as well as that of eclipses and planetary conjunctions, was in relation to astrology. Reform, however, was obviously in the air.
The doctrine of Copernicus was destined very soon to divide others besides the Lutheran leaders. The leaven of inquiry was working, and not long
after the death of Copernicus real advances were to come, first in the accuracy of observations, and, as a necessary result of these, in the planetary
theory itself.

CHAPTER II.

EARLY LIFE OF KEPLER.

On 21st December, 1571, at Weil in the Duchy of Wurtemberg, was born a weak and sickly seven-months’ child, to whom his parents

Henry and Catherine Kepler gave the name of John. Henry Kepler was a petty officer in the service of the reigning Duke, and in 1576 joined the
army serving in the Netherlands. His wife followed him, leaving her young son in his grandfather’s care at Leonberg, where he barely recovered
from a severe attack of smallpox. It was from this place that John derived the Latinised name of Leonmontanus, in accordance with the common
practice of the time, but he was not known by it to any great extent. He was sent to school in 1577, but in the following year his father returned to
Germany, almost ruined by the absconding of an acquaintance for whom he had become surety. Henry Kepler was obliged to sell his house and
most of his belongings, and to keep a tavern at Elmendingen, withdrawing his son from school to help him with the rough work. In 1583 young
Kepler was sent to the school at Elmendingen, and in 1584 had another narrow escape from death by a violent illness. In 1586 he was sent, at the
charges of the Duke, to the monastic school of Maulbronn; from whence, in accordance with the school regulations, he passed at the end of his
first year the examination for the bachelor’s degree at Tübingen, returning for two more years as a “veteran” to Maulbronn before being admitted
as a resident student at Tübingen. The three years thus spent at Maulbronn were marked by recurrences of several of the diseases from which he
had suffered in childhood, and also by family troubles at his home. His father went away after a quarrel with his wife Catherine, and died abroad.
Catherine herself, who seems to have been of a very unamiable disposition, next quarrelled with her own relatives. It is not surprising therefore that
Kepler after taking his M.A. degree in August, 1591, coming out second in the examination lists, was ready to accept the first appointment offered
him, even if it should involve leaving home. This happened to be the lectureship in astronomy at Gratz, the chief town in Styria. Kepler’s knowledge
of astronomy was limited to the compulsory school course, nor had he as yet any particular leaning towards the science; the post, moreover, was a
meagre and unimportant one. On the other hand he had frequently expressed disgust at the way in which one after another of his companions had
refused “foreign” appointments which had been arranged for them under the Duke’s scheme of education. His tutors also strongly urged him to
accept the lectureship, and he had not the usual reluctance to leave home. He therefore proceeded to Gratz, protesting that he did not thereby
forfeit his claim to a more promising opening, when such should appear. His astronomical tutor, Maestlin, encouraged him to devote himself to his
newly adopted science, and the first result of this advice appeared before very long in Kepler’s “Mysterium Cosmographicum”. The bent of his
mind was towards philosophical speculation, to which he had been attracted in his youthful studies of Scaliger’s “Exoteric Exercises”. He says he
devoted much time “to the examination of the nature of heaven, of souls, of genii, of the elements, of the essence of fire, of the cause of fountains,
the ebb and flow of the tides, the shape of the continents and inland seas, and things of this sort”. Following his tutor in his admiration for the
Copernican theory, he wrote an essay on the primary motion, attributing it to the rotation of the earth, and this not for the mathematical reasons
brought forward by Copernicus, but, as he himself says, on physical or metaphysical grounds. In 1595, having more leisure from lectures, he

turned his speculative mind to the number, size, and motion of the planetary orbits. He first tried simple numerical relations, but none of them
appeared to be twice, thrice, or four times as great as another, although he felt convinced that there was some relation between the motions and
the distances, seeing that when a gap appeared in one series, there was a corresponding gap in the other. These gaps he attempted to fill by
hypothetical planets between Mars and Jupiter, and between Mercury and Venus, but this method also failed to provide the regular proportion
which he sought, besides being open to the objection that on the same principle there might be many more equally invisible planets at either end of
the series. He was nevertheless unwilling to adopt the opinion of Rheticus that the number six was sacred, maintaining that the “sacredness” of the
number was of much more recent date than the creation of the worlds, and could not therefore account for it. He next tried an ingenious idea,
comparing the perpendiculars from different points of a quadrant of a circle on a tangent at its extremity. The greatest of these, the tangent, not
being cut by the quadrant, he called the line of the sun, and associated with infinite force. The shortest, being the point at the other end of the
quadrant, thus corresponded to the fixed stars or zero force; intermediate ones were to be found proportional to the “forces” of the six planets.
After a great amount of unfinished trial calculations, which took nearly a whole summer, he convinced himself that success did not lie that way. In
July, 1595, while lecturing on the great planetary conjunctions, he drew quasi-triangles in a circular zodiac showing the slow progression of these
points of conjunction at intervals of just over 240° or eight signs. The successive chords marked out a smaller circle to which they were tangents,
about half the diameter of the zodiacal circle as drawn, and Kepler at once saw a similarity to the orbits of Saturn and Jupiter, the radius of the
inscribed circle of an equilateral triangle being half that of the circumscribed circle. His natural sequence of ideas impelled him to try a square, in the
hope that the circumscribed and inscribed circles might give him a similar “analogy” for the orbits of Jupiter and Mars. He next tried a pentagon
and so on, but he soon noted that he would never reach the sun that way, nor would he find any such limitation as six, the number of “possibles”
being obviously infinite. The actual planets moreover were not even six but only five, so far as he knew, so he next pondered the question of what
sort of things these could be of which only five different figures were possible and suddenly thought of the five regular solids. [2] He immediately
pounced upon this idea and ultimately evolved the following scheme. “The earth is the sphere, the measure of all; round it describe a
dodecahedron; the sphere including this will be Mars. Round Mars describe a tetrahedron; the sphere including this will be Jupiter. Describe a
cube round Jupiter; the sphere including this will be Saturn. Now, inscribe in the earth an icosahedron, the sphere inscribed in it will be Venus:
inscribe an octahedron in Venus: the circle inscribed in it will be Mercury.” With this result Kepler was inordinately pleased, and regretted not a
moment of the time spent in obtaining it, though to us this “Mysterium Cosmographicum” can only appear useless, even without the more recent
additions to the known planets. He admitted that a certain thickness must be assigned to the intervening spheres to cover the greatest and least
distances of the several planets from the sun, but even then some of the numbers obtained are not a very close fit for the corresponding planetary
orbits. Kepler’s own suggested explanation of the discordances was that they must be due to erroneous measures of the planetary distances, and
this, in those days of crude and infrequent observations, could not easily be disproved. He next thought of a variety of reasons why the five regular
solids should occur in precisely the order given and in no other, diverging from this into a subtle and not very intelligible process of reasoning to
account for the division of the zodiac into 360°. The next subject was more important, and dealt with the relation between the distances of the
planets and their times of revolution round the sun. It was obvious that the period was not simply proportional to the distance, as the outer planets
were all too slow for this, and he concluded “either that the moving intelligences of the planets are weakest in those that are farthest from the sun,
or that there is one moving intelligence in the sun, the common centre, forcing them all round, but those most violently which are nearest, and that it
languishes in some sort and grows weaker at the most distant, because of the remoteness and the attenuation of the virtue”. This is not so near a
guess at the theory of gravitation as might be supposed, for Kepler imagined that a repulsive force was necessary to account for the planets being
sometimes further from the sun, and so laid aside the idea of a constant attractive force. He made several other attempts to find a law connecting
the distances and periods of the planets, but without success at that time, and only desisted when by unconsciously arguing in a circle he appeared
to get the same result from two totally different hypotheses. He sent copies of his book to several leading astronomers, of whom Galileo praised his
ingenuity and good faith, while Tycho Brahe was evidently much struck with the work and advised him to adapt something similar to the Tychonic
system instead of the Copernican. He also intimated that his Uraniborg observations would provide more accurate determinations of the planetary
orbits, and thus made Kepler eager to visit him, a project which as we shall see was more than fulfilled. Another copy of the book Kepler sent to
Reymers the Imperial astronomer with a most fulsome letter, which Tycho, who asserted that Reymers had simply plagiarised his work, very
strongly resented, thus drawing from Kepler a long letter of apology. About the same time Kepler had married a lady already twice widowed, and
become involved in difficulties with her relatives on financial grounds, and with the Styrian authorities in connection with the religious disputes then
coming to a head. On account of these latter he thought it expedient, the year after his marriage, to withdraw to Hungary, from whence he sent
short treatises to Tübingen, “On the magnet” (following the ideas of Gilbert of Colchester), “On the cause of the obliquity of the ecliptic” and “On
the Divine wisdom as shown in the Creation”. His next important step makes it desirable to devote a chapter to a short notice of Tycho Brahe.

Footnote 2: Since the sum of the plane angles at a corner of a regular solid must be less than four right angles, it is easily seen that few regular solids are possible. Hexagonal
faces are clearly impossible, or any polygonal faces with more than five sides. The possible forms are the dodecahedron with twelve pentagonal faces, three meeting at each
corner; the cube, six square faces, three meeting at each corner; and three figures with triangular faces, the tetrahedron of four faces, three meeting at each corner; the octahedron
of eight faces, four meeting at each corner; and the icosahedron of twenty faces, five meeting at each corner.

CHAPTER III.

TYCHO BRAHE.

The age following that of Copernicus produced three outstanding figures associated with the science of astronomy, then reaching the close of

what Professor Forbes so aptly styles the geometrical period. These three Sir David Brewster has termed “Martyrs of Science”; Galileo, the great
Italian philosopher, has his own place among the “Pioneers of Science”; and invaluable though Tycho Brahe’s work was, the latter can hardly be
claimed as a pioneer in the same sense as the other two. Nevertheless, Kepler, the third member of the trio, could not have made his most valuable
discoveries without Tycho’s observations.

Of noble family, born a twin on 14th December, 1546, at Knudstrup in Scania (the southernmost part of Sweden, then forming part of the

kingdom of Denmark), Tycho was kidnapped a year later by a childless uncle. This uncle brought him up as his own son, provided him at the age
of seven with a tutor, and sent him in 1559 to the University of Copenhagen, to study for a political career by taking courses in rhetoric and
philosophy. On 21st August, 1560, however, a solar eclipse took place, total in Portugal, and therefore of small proportions in Denmark, and
Tycho’s keen interest was awakened, not so much by the phenomenon, as by the fact that it had occurred according to prediction. Soon
afterwards he purchased an edition of Ptolemy in order to read up the subject of astronomy, to which, and to mathematics, he devoted most of the
remainder of his three years’ course at Copenhagen. His uncle next sent him to Leipzig to study law, but he managed to continue his astronomical
researches. He obtained the Alphonsine and the new Prutenic Tables, but soon found that the latter, though more accurate than the former, failed
to represent the true positions of the planets, and grasped the fact that continuous observation was essential in order to determine the true motions.
He began by observing a conjunction of Jupiter and Saturn in August, 1563, and found the Prutenic Tables several days in error, and the
Alphonsine a whole month. He provided himself with a cross-staff for determining the angular distance between stars or other objects, and, finding
the divisions of the scale inaccurate, constructed a table of corrections, an improvement that seems to have been a decided innovation, the previous
practice having been to use the best available instrument and ignore its errors. About this time war broke out between Denmark and Sweden, and
Tycho returned to his uncle, who was vice-admiral and attached to the king’s suite. The uncle died in the following month, and early in the next
year Tycho went abroad again, this time to Wittenberg. After five months, however, an outbreak of plague drove him away, and he matriculated at
Rostock, where he found little astronomy but a good deal of astrology. While there he fought a duel in the dark and lost part of his nose, which he
replaced by a composition of gold and silver. He carried on regular observations with his cross-staff and persevered with his astronomical studies
in spite of the objections and want of sympathy of his fellow-countrymen. The King of Denmark, however, having a higher opinion of the value of
science, promised Tycho the first canonry that should fall vacant in the cathedral chapter of Roskilde, so that he might be assured of an income
while devoting himself to financially unproductive work. In 1568 Tycho left Rostock, and matriculated at Basle, but soon moved on to Augsburg,
where he found more enthusiasm for astronomy, and induced one of his new friends to order the construction of a large 19-foot quadrant of heavy
oak beams. This was the first of the series of great instruments associated with Tycho’s name, and it remained in use for five years, being
destroyed by a great storm in 1574. Tycho meanwhile had left Augsburg in 1570 and returned to live with his father, now governor of Helsingborg
Castle, until the latter’s death in the following year. Tycho then joined his mother’s brother, Steen Bille, the only one of his relatives who showed
any sympathy with his desire for a scientific career.

On 11th November, 1572, Tycho noticed an unfamiliar bright star in the constellation of Cassiopeia, and continued to observe it with a

sextant. It was a very brilliant object, equal to Venus at its brightest for the rest of November, not falling below the first magnitude for another four
months, and remaining visible for more than a year afterwards. Tycho wrote a little book on the new star, maintaining that it had practically no
parallax, and therefore could not be, as some supposed, a comet. Deeming authorship beneath the dignity of a noble he was very reluctant to
publish, but he was convinced of the importance of increasing the number and accuracy of observations, though he was by no means free from all
the erroneous ideas of his time. The little book contained a certain amount of astrology, but Tycho evidently did not regard this as of very great
importance. He adopted the view that the very rarity of the phenomenon of a new star must prevent the formulation and adoption of definite rules
for determining its significance. We gather from lectures which he was persuaded to deliver at the University of Copenhagen that, though in
agreement with the accepted canons of astrology as to the influence of planetary conjunctions and such phenomena on the course of human events,
he did not consider the fate predicted by anyone’s horoscope to be unavoidable, but thought the great value of astrology lay in the warnings
derived from such computations, which should enable the believer to avoid threatened calamities. In 1575 he left Denmark once more and made
his way to Cassel, where he found a kindred spirit in the studious Landgrave, William IV. of Hesse, whose astronomical pursuits had been
interrupted by his accession to the government of Hesse, in 1567. Tycho observed with him for some time, the two forming a firm friendship, and
then visited successively Frankfort, Basle, and Venice, returning by way of Augsburg, Ratisbon, and Saalfeld to Wittenberg; on the way he
acquired various astronomical manuscripts, made friends among practical astronomers, and examined new instruments. He seemed to have
considered the advantages of the several places thus visited and decided on Basle, but on his return to Denmark to fetch his family with the object
of transferring them to Basle, he found that his friend the Landgrave had written to King Frederick on his behalf, urging him to provide the means to
enable Tycho to pursue his astronomical work, promising that not only should credit result for the king and for Denmark but that science itself
would be greatly advanced. The ultimate result of this letter was that after refusing various offers, Tycho accepted from the king a grant of the small
island of Hveen, in the Sound, with a guaranteed income, in addition to a large sum from the treasury for building an observatory on the island, far
removed from the distractions of court life. Here Tycho built his celebrated observatory of Uraniborg and began observations in December, 1576,
using the large instruments then found necessary in order to attain the accuracy of observation which within the next half-century was to be so
greatly facilitated by the invention of the telescope. Here also he built several smaller observing rooms, so that his pupils should be able to observe
independently. For more than twenty years he continued his observations at Uraniborg, surrounded by his family, and attracting numerous pupils.
His constant aim was to accumulate a large store of observations of a high order of accuracy, and thus to provide data for the complete reform of
astronomy. As we have seen, few of the Danish nobles had any sympathy with Tycho’s pursuits, and most of them strongly resented the continual
expense borne by the King’s treasury. Tycho moreover was so absorbed in his scientific pursuits that he would not take the trouble to be a good
landlord, nor to carry out all the duties laid upon him in return for certain of his grants of income. His buildings included a chemical laboratory, and
he was in the habit of making up elixirs for various medical purposes; these were quite popular, particularly as he made no charge for them. He
seems to have been something of a homœopathist, for he recommends sulphur to cure infectious diseases “brought on by the sulphurous vapours of
the Aurora Borealis”!

King Frederick, in consideration of various grants to Tycho, relied upon his assistance in scientific matters, and especially in astrological

calculations; such as the horoscope of the heir apparent, Prince Christian, born in 1577, which has been preserved among Tycho’s writings. There
is, however, no known copy in existence of any of the series of annual almanacs with predictions which he prepared for the King. In November,
1577, appeared a bright comet, which Tycho carefully observed with his sextant, proving that it had no perceptible parallax, and must therefore be
further off than the moon. He thus definitely overthrew the common belief in the atmospheric origin of comets, which he had himself hitherto shared.

With increasing accuracy he observed several other comets, notably one in 1585, when he had a full equipment of instruments and a large staff of
assistants. The year 1588, which saw the death of his royal benefactor, saw also the publication of a volume of Tycho’s great work “Introduction
to the New Astronomy”. The first volume, devoted to the new star of 1572, was not ready, because the reduction of the observations involved so
much research to correct the star places for refraction, precession, etc.; it was not completed in fact until Tycho’s death, but the second volume,
dealing with the comet of 1577, was printed at Uraniborg and some copies were issued in 1588. Besides the comet observations it included an
account of Tycho’s system of the world. He would not accept the Copernican system, as he considered the earth too heavy and sluggish to move,
and also that the authority of Scripture was against such an hypothesis. He therefore assumed that the other planets revolved about the sun, while
the sun, moon, and stars revolved about the earth as a centre. Geometrically this is much the same as the Copernican system, but physically it
involves the grotesque demand that the whole system of stars revolves round our insignificant little earth every twenty-four hours. Since his
previous small book on the comet, Tycho had evidently considered more fully its possible astrological significance, for he foretold a religious war,
giving the date of its commencement, and also the rising of a great Protestant champion. These predictions were apparently fulfilled almost to the
letter by the great religious wars that broke out towards the end of the sixteenth century, and in the person of Gustavus Adolphus.

King Frederick’s death did not at first affect Tycho’s position, for the new king, Christian, was only eleven years old, and for some years the

council of regents included two of his supporters. After their deaths, however, his emoluments began to be cut down on the plea of economy, and
as he took very little trouble to carry out any other than scientific duties it was easy enough for his enemies to find fault. One after another source of
income was cut off, but he persevered with his scientific work, including a catalogue of stars. He had obtained plenty of good observations of 777
stars, but thought his catalogue should contain 1000 stars, so he hastily observed as many more as he could up to the time of his leaving Hveen,
though even then he had not completed his programme. About the time that King Christian reached the age of eighteen, Tycho began to look about
for a new patron, and to consider the prospects offered by transferring himself with his instruments and activities to the patronage of the Emperor
Rudolph II. In 1597, when even his pension from the Royal treasury was cut off, he hurriedly packed up his instruments and library, and after a
few weeks’ sojourn at Copenhagen, proceeded to Rostock, in Mecklenburg, whence he sent an appeal to King Christian. It is possible that had
he done this before leaving Hveen it might have had more effect, but it can be readily seen from the tone of the king’s unfavourable reply that his
departure was regarded as an aggravation of previous shortcomings. Driven from Rostock by the plague, Tycho settled temporarily at
Wandsbeck, in Holstein, but towards the end of 1598 set out to meet the Emperor at Prague. Once more plague intervened and he spent some
time at Dresden, afterwards going to Wittenberg for the winter. He ultimately reached Prague in June, 1599. Rudolph granted him a salary of at
least 3000 florins, promising also to settle on him the first hereditary estate that should lapse to the Crown. He offered, moreover, the choice
between three castles outside Prague, of which Tycho chose Benatek. There he set about altering the buildings in readiness for his instruments, for
which he sent to Uraniborg. Before they reached him, after many vexatious delays, he had given up waiting for the funds promised for his building
expenses, and removed from Benatek to Prague. It was during this interval that after considerable negotiation, Kepler, who had been in
correspondence with Tycho, consented to join him as an assistant. Another assistant, Longomontanus, who had been with Tycho at Uraniborg,
was finding difficulty with the long series of Mars observations, and it was arranged that he should transfer his energies to the lunar observations,
leaving those of Mars for Kepler. Before very much could be done with them, however, Tycho died at the end of October, 1601. He may have
regretted the peaceful island of Hveen, considering the troubles in which Bohemia was rapidly becoming involved, but there is little doubt that had it
not been for his self-imposed exile, his observations would not have come into Kepler’s hands, and their great value might have been lost. In any
case it was at Uraniborg that the mass of observations was produced upon which the fame of Tycho Brahe rests. His own discoveries, though in
themselves the most important made in astronomy for many centuries, are far less valuable than those for which his observations furnished the
material. He discovered the third and fourth inequalities of the moon in longitude, called respectively the variation and the annual equation, also the
variability of the motion of the moon’s nodes and the inclination of its orbit to the ecliptic. He obtained an improved value of the constant of
precession, and did good service by rejecting the idea that it was variable, an idea which, under the name of trepidation, had for many centuries
been accepted. He discovered the effect of refraction, though only approximately its amount, and determined improved values of many other
astronomical constants, but singularly enough made no determination of the distance of the sun, adopting instead the ancient and erroneous value
given by Hipparchus.

His magnificent Observatory of Uraniborg, the finest building for astronomical purposes that the world had hitherto seen, was allowed to fall

into decay, and scarcely more than mere indications of the site may now be seen.

CHAPTER IV.

KEPLER JOINS TYCHO.

The association of Kepler with Tycho was one of the most important landmarks in the history of astronomy. The younger man hoped, by the

aid of Tycho’s planetary observations, to obtain better support for some of his fanciful speculative theories, while the latter, who had certainly not
gained in prestige by leaving Denmark, was in great need of a competent staff of assistants. Of the two it would almost seem that Tycho thought
himself the greater gainer, for in spite of his reputation for brusqueness and want of consideration, he not only made light of Kepler’s apology in the
matter of Reymers, but treated him with uniform kindness in the face of great rudeness and ingratitude. He begged him to come “as a welcome
friend,” though Kepler, very touchy on the subject of his own astronomical powers, was afraid he might be regarded as simply a subordinate
assistant. An arrangement had been suggested by which Kepler should obtain two years’ leave of absence from Gratz on full pay, which, because
of the higher cost of living in Prague, should be supplemented by the Emperor; but before this could be concluded, Kepler threw up his

professorship, and thinking he had thereby also lost the chance of going to Prague, applied to Maestlin and others of his Tübingen friends to make
interest for him with the Duke of Wurtemberg and secure the professorship of medicine. Tycho, however, still urged him to come to Prague,
promising to do his utmost to secure for him a permanent appointment, or in any event to see that he was not the loser by coming. Kepler was
delayed by illness on the way, but ultimately reached Prague, accompanied by his wife, and for some time lived entirely at Tycho’s expense, writing
by way of return essays against Reymers and another man, who had claimed the credit of the Tychonic system. This Kepler could do with a clear
conscience, as it was only a question of priority and did not involve any support of the system, which he deemed far inferior to that of Copernicus.
The following year saw friction between the two astronomers, and we learn from Kepler’s abject letter of apology that he was entirely in the
wrong. It was about money matters, which in one way or another embittered the rest of Kepler’s life, and it arose during his absence from Prague.
On his return in September, 1601, Tycho presented him to the Emperor, who gave him the title of Imperial Mathematician, on condition of
assisting Tycho in his calculations, the very thing Kepler was most anxious to be allowed to do: for nowhere else in the world was there such a
collection of good observations sufficient for his purpose of reforming the whole theory of astronomy. The Emperor’s interest was still mainly with
astrology, but he liked to think that his name would be handed down to posterity in connection with the new Planetary Tables in the same way as
that of Alphonso of Castile, and he made liberal promises to pay the expenses. Tycho’s other principal assistant, Longomontanus, did not stay long
after giving up the Mars observations to Kepler, but instead of working at the new lunar theory, suddenly left to take up a professorship of
astronomy in his native Denmark. Very shortly afterwards Tycho himself died of acute distemper; Kepler began to prepare the mass of
manuscripts for publication, but, as everything was claimed by the Brahe family, he was not allowed to finish the work. He succeeded to Tycho’s
post of principal mathematician to the Emperor, at a reduced official salary, which owing to the emptiness of the Imperial treasury was almost
always in arrear. In order to meet his expenses he had recourse to the casting of nativities, for which he gained considerable reputation and
received very good pay. He worked by the conventional rules of astrology, and was quite prepared to take fees for so doing, although he had very
little faith in them, preferring his own fanciful ideas.

In 1604 the constellation of Cassiopeia was once more temporarily enriched by the appearance of a new star, said by some to be brighter

than Tycho’s nova, and by others to be twice as bright as Jupiter. Kepler at once wrote a short account of it, from which may be gathered some
idea of his attitude towards astrology. Contrasting the two novae, he says: “Yonder one chose for its appearance a time no way remarkable, and
came into the world quite unexpectedly, like an enemy storming a town and breaking into the market-place before the citizens are aware of his
approach; but ours has come exactly in the year of which astrologers have written so much about the fiery trigon that happens in it; just in the
month in which (according to Cyprian), Mars comes up to a very perfect conjunction with the other two superior planets; just in the day when
Mars has joined Jupiter, and just in the region where this conjunction has taken place. Therefore the apparition of this star is not like a secret
hostile irruption, as was that one of 1572, but the spectacle of a public triumph, or the entry of a mighty potentate; when the couriers ride in some
time before to prepare his lodgings, and the crowd of young urchins begin to think the time over long to wait, then roll in, one after another, the
ammunition and money, and baggage waggons, and presently the trampling of horse and the rush of people from every side to the streets and
windows; and when the crowd have gazed with their jaws all agape at the troops of knights; then at last the trumpeters and archers and lackeys so
distinguish the person of the monarch, that there is no occasion to point him out, but every one cries of his own accord—‘Here we have him’.
What it may portend is hard to determine, and this much only is certain, that it comes to tell mankind either nothing at all or high and mighty news,
quite beyond human sense and understanding. It will have an important influence on political and social relations; not indeed by its own nature, but
as it were accidentally through the disposition of mankind. First, it portends to the booksellers great disturbances and tolerable gains; for almost
every Theologus, Philosophicus, Medicus, and Mathematicus, or whoever else, having no laborious occupation entrusted to him, seeks his
pleasure in studiis, will make particular remarks upon it, and will wish to bring these remarks to the light. Just so will others, learned and
unlearned, wish to know its meaning, and they will buy the authors who profess to tell them. I mention these things merely by way of example,
because although thus much can be easily predicted without great skill, yet may it happen just as easily, and in the same manner, that the vulgar, or
whoever else is of easy faith, or, it may be, crazy, may wish to exalt himself into a great prophet; or it may even happen that some powerful lord,
who has good foundation and beginning of great dignities, will be cheered on by this phenomenon to venture on some new scheme, just as if God
had set up this star in the darkness merely to enlighten them.” He made no secret of his views on conventional astrology, as to which he claimed to
speak with the authority of one fully conversant with its principles, but he nevertheless expressed his sincere conviction that the conjunctions and
aspects of the planets certainly did affect things on the earth, maintaining that he was driven to this belief against his will by “most unfailing
experiences”.

Meanwhile the projected Rudolphine Tables were continually delayed by the want of money. Kepler’s nominal salary should have been

ample for his expenses, increased though they were by his growing family, but in the depleted state of the treasury there were many who objected
to any payment for such “unpractical” purposes. This particular attitude has not been confined to any spec...